package LC;

import java.util.ArrayList;
import java.util.List;

/**
 * https://leetcode.com/problems/gray-code/description/
 * The gray code is a binary numeral system where two successive values differ in only one bit.
 * Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code.
 * A gray code sequence must begin with 0.
 * For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:
 * 00 - 0
 * 01 - 1
 * 11 - 3
 * 10 - 2
 * Note:
 * For a given n, a gray code sequence is not uniquely defined.
 * For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.
 * For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.
 */
public class LC_089_GrayCode_Recur_BackTracking {
    public static void main(String[] args) {
        System.out.println(Solution.grayCode(2));
    }

    static class Solution {
        static List<Integer> grayCode(int n) {
            if (n == 0) {
                List<Integer> list = new ArrayList<>();
                list.add(0);
                return list;
            }
            if (n == 1) {
                List<Integer> list = new ArrayList<>();
                list.add(0);
                list.add(1);
                return list;
            }

            List<Integer> grayM = grayCode(n - 1);
            List<Integer> list = new ArrayList<>();

            for (int i = 0; i < Math.pow(2, n); i++) {
                if (i < Math.pow(2, n - 1))
                    list.add(grayM.get(i));
                else
                    list.add(grayM.get((int) Math.pow(2, n) - i - 1) + (int) Math.pow(2, n - 1));
            }
            return list;
        }
    }
}
